The movie seems to end effectively with Brigid descending on the elevator with shadows of the gate seeming to symbolize the bars she will be living behind for the next twenty years, assuming she gets off with a life sentence rather than hanging. This scene was easy to shoot in a movie but wouldn't have been so effective as the last scene in the novel. Iva does not have as strong a role in the movie as in the book, so it may not have been felt necessary to do something with her character at the end. In the book the reader is left wondering what Spade will do about Iva, now that her husband is disposed of and they do not have to be furtive about their relationship. The reader probably hopes Spade will break up with her as soon as Effie sends her into his office. He could use the excuse that he can't forgive her for sending the police to his apartment when Brigid was there. He obviously doesn't want to see her. The last words in the story are:
"Yes," he said, and shivered. "Well, send her in."
He probably shivers because he realizes she has more of a hold on him now that Miles is dead and Spade is cleared of his partner's murder. John Huston was wise to get rid of that final business with Iva because it seems to open another whole story. He had to include Iva in the movie because it was her relationship with Spade that made the police suspect him of murdering Miles. She could conceivably cause him more trouble (in the book) if he didn't handle her with tact. She could go back to the police and accuse him of something else. She is potential trouble. She will undoubtedly cling to him like the ivy her name resembles.
In the book the reader is left wondering what will happen with Sppade and Iva, but in the movie the viewer is not left wondering about Iva at all.